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## Finding Focus for Mathematics Instruction Grades 3-5

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**Thumb-Area Student Achievement Model and Huron Intermediate**School District Finding Focus for Mathematics Instruction Grades 3-5 February 8, 2010 Huron Area Technical Center February 22, 2010 Tuscola Technology Center**Today’s Goals**• Become familiar with Mathematics Curriculum • Deepen understanding of Big Math Ideas • Use strategies for explicit vocabulary instruction • Understand instructional implications of research • Use assessment in a 3-tier process • Support instruction for intervention and enrichment**Be Thinking About**• What is one idea you will try in the next week? • What are 2-3 items you will share or discuss with your colleagues? • How will that happen?**What Do the Focal Points Look Like?**• Work in grade-level teams. • Find the focal points for your grade. • Sort the GLCE topics according to focal point. Make a separate pile for “leftover topics.” Compare your sort to MDE list. Re-arrange if necessary.**How Should the Focal Points Impact Instruction?**• Based on nationally-recognized topics • Related to GLCEs and MEAP: • Core expectations • Must be related to a focal point • No more than 20 per grade • Assessed with two items, all students • Extended core expectations • Not related to a focal point • Assessed with no more than one item (sampled)**Discussion**• 70-80% of instruction should focus on GLCEs related to focal points. Use your textbook to think about your instruction. What topics should be emphasized more? Less?**Useful Documents**• Math GLCEs Assessed with NC Designations • www.mi.gov/mathematics • Mathematics Focal Points K-8 Alignment (11-11-09 from SAM) • http://www.hisd.k12.mi.us/SAM/main.html**Common Core Standards Initiative DRAFT 1-13-2010**• Match CCSI standards to Focal Points and GLCEs • Make new piles if needed • No GLCE for a CCSI standard? Check another grade.**Compare Focal Point GLCEs to CCSI Number and Operations**• Similar topics (multiplication/division; fractions) • Addition of fractions in CCSI Grade 4 (not a Grade 4 focal point) • Multiplication and division of fractions in CCSI Grade 5 (not a Grade 5 focal point)**Only 24% of 13-year-olds correctly estimated the sum of**12/13 + 7/8 to be 2 - Carpenter and Corbitt**The answers to this question show that students do not**understand fraction notation and suggest that we should not teach operations with fractions until students can describe fraction amounts and compare them to familiar benchmarks such as 1/2 and 1. - Carpenter and Corbitt**¾ + ½**• Only 35% of 13-year-olds answered correctly**Before operating with fractions, students need to understand**what a fraction means. This involves understanding the part-whole model for fractions and the ability to judge the relative size of a fraction. - Cramer et. al (2008) p. 492**This fall, only 69% of SAM sixth-graders were proficient on**a rational computation measure**Fraction Focal Points Grades 3-5**• Grade 3: Developing an understanding of fractions and fraction equivalence • Grade 4: Developing an understanding of fractions and decimals, including the connections between them • Grade 5: Developing an understanding of and fluency with addition and subtraction of fractions and decimals**Think - Write**• What are the critical fraction ideas for the grade you teach?**Read the introduction.**• Share with a neighbor.**How many focal points are at your grade level?**• The GLCE topics are the same as the Core and Extended Designations document from MDE**National Math Panel Benchmarks are checkpoints**• Benchmarks are often a grade or two past where the topic is typically taught**Find this chart for each focal point at your grade.**• The columns are the same as the 11” x 17” K-8 Alignment chart**Three Sections for Each Focal Point**From the 1-13-2010 DRAFT of the Common Core Standards Initiative**Explore the Finding Focus Document**• There are two places in this document to find the list of GLCE topics for focal a point. Where are those two places? • Find the “leftover” GLCEs for your grade. Compare the chart to the 11” x 17” K-8 Alignment. • Find the fractions focal point for your grade. What number is it? • How many “Extended Core” expectations are related to the fraction focal point? • Choose any focal point at your grade. Compare the GLCEs for the focal point to the DRAFT CCSI standards.**The Big Ideas are NOT**Topics for instructional planning GLCEs for assessing students The Big Ideas ARE The mathematics YOU should keep in mind as you plan instruction Critical ideas that are true at all grade levels Big Mathematical Ideas and Understandings**SILENT Reading**• Find the “Big Mathematical Ideas and Understandings” for the fraction focal point at your grade • Read, re-read, highlight, and take notes • Add to the list you brainstormed of critical fraction ideas for your grade**Big Ideas for Fractions**With your grade level, discuss • What stood out to you from the Big Ideas? • What questions do you still have? • Revise your notes.**Rational Number**Projecthttp://www.cehd.umn.edu/rationalnumberproject/ • From the home page, scroll down and choose “publications in chronological order” • Two documents released 2009: • RNP1 – “Initial Fraction Ideas” • RNP2 – “Fraction Operations and Initial Decimal Ideas”**Order 3/4 and 14/15.**• Which fraction is closer to 1? How do you know? • One student suggested the two fractions are equal because both are one piece away from the whole. What do you think? • Verify your conclusion by modeling each fraction with fraction circles.**Common Misunderstandings**• Both are equal, as both are one away from the whole • ¾ is larger because the denominator is a lower number so it is going to have bigger pieces**Order 4/5 and 8/9**• Do NOT find a common denominator or decimal equivalents • Use numerical reasoning and fraction circles to justify your answer**Summary**• You can judge the relative size of fractions by thinking about fraction circles. • Using ½ as a benchmark is helpful. • Thinking about how close a fraction is to one whole is also helpful when comparing fractions like 3 and 5 or 4 and 99. 4 6 5 100**Lesson 1 (RNP2, 2009) Student Pages A-D**• Each person complete a different page • At your table, discuss • The purpose of each page • Student misunderstandings to expect**What do you think of this student’s reasoning?**Does this student’s strategy work for 9 and 98 ? 10 100**Math Vocabulary**• Targeted Vocabulary with Focal Points on Page 5 • Suggested Vocabulary at end of document How would you describe each list? How would you use each list?**Importance of Explicit Vocabulary Instruction**Find “Targeted Vocabulary” on Page 5**Fraction**• frac’ tion • (FRAC shun) • Latin root: frangere “to break” • What word might have the same root? • “fracture” also comes from the Latin frangere**fraction: a number that can be expressed in the**form , where a and b are whole numbers (b≠0). • Examples and non-examples • Multiple examples fraction Any connection Alternate Idea: Story problem with matching equation**Explicit Vocabulary Instruction – Word Banks**• Students see relationships between words • Students practice using math language**Denominator**• What words relate to denominator? • How would you introduce the term in a way that activates activate students’ prior knowledge?**Create a word bank for denominator**• Share at your table**Choose a targeted vocabulary term for your grade**Complete one of the strategies for the word (word map, word bank, or breaking down the definition)**Textbook Analysis**• How does your textbook present new terms? • Does the teacher’s guide include any strategies for explicit vocabulary instruction?